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Game theory in the popular press.

Phage-lift for game theory

News and Views
Martin A. Nowak and Karl Sigmund
April 1, 1999
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The prisoner's dilemma is a classic of game theory in which acting for individual advantage is pitted against acting for collective benefit. An example has been identified among clones of a virus that infects bacteria.

A virus is a natural-born cheat that makes its living by exploiting the vital functions of a host cell. Small wonder, then, that viruses also exploit each other. By neatly combining theory and experiments, Turner and Chao (page 441 of this issue) have managed to demonstrate that certain phages — viruses that infect bacteria — actually engage in the prisoner's dilemma, that archetypal trap between cooperation and non-cooperation. Evolutionary game theorists will see this paper as a landmark. Indeed, it will be difficult to find players more primitive than the phage 6 and its mutant clone H2, stubby chunks of RNA that for their replication depend on a bacterial cell, and are therefore the subject of learned discussions as to whether they constitute life or not.

The prisoner's dilemma was devised by game theorists barely 50 years ago. Today, it seems difficult to conceive how moral philosophers, political thinkers or evolutionary biologists could ever have managed without it. It is not much of a game, to be honest. Two players each have two options, to cooperate or not cooperate (defect). If both cooperate, they receive a reward, R, which is larger than the punishment, P, obtained if both defect. If one defects and the other cooperates, the defector obtains a payoff, T (the temptation), which is greater than R, and the cooperator receives the sucker's payoff S, which is less than P. So T R > P > S. Because it pays more to defect, no matter whether the other cooperates or not, a rational player is bound to defect. Two rational players, therefore, will each end up with payoff P, instead of the reward R. Lowly 6 usually does better and achieves the reward, so one might wonder whether rationality is really the gift it is supposed to be.

As the exemplar for the clash between individual advantage and collective benefit, the prisoner's dilemma was originally used to study the concept of rational choice, and to test actual human behaviour. In 1981, in a seminal paper by Axelrod and Hamilton, it was applied to the evolution of cooperation in biological societies. Axelrod and Hamilton used computer simulations to display the emergence of cooperation in artificial populations, and suggested a wealth of biological examples, ranging from hairless primates engaged in trench warfare to bacteria living in their guts, in which the principles of the prisoner's dilemma might apply.

In the following years, both computer simulations and study of real-life occurrences of the prisoner's dilemma were expanding areas of research, but they did not grow at an equal pace. It proved much easier to do the simulations, and the empirical evidence lagged sadly behind. The same handful of examples were invoked time and again: vervet monkeys uttering alarm calls, sticklebacks and guppies engaged in predator inspection, vampire bats feeding their hungry fellows. In most cases, the jury is still out on whether these are bona fide instances of the prisoner's dilemma. The underlying problem is the bug-bear of evolutionary game theory: the currency for the payoff values is Darwinian fitness, which is notoriously difficult to measure for monkeys hiding in the bush, bats clustering in cave-roofs, and fish darting in and out of shoals.

With phages, the job becomes doable. The two strategies are embodied in the usual type of PHI-6 (the cooperator), and a mutant called PHI-H2 (the defector) which manufactures fewer of the intracellular products needed for replication of the phages. Turner and Chao measured the relative fitness of the two types in bacterial cultures by means of a genetic marker, cleverly exploiting the fact that the defectors' fitness is greater when they are rare. If the fitness of a PHI-6 phage in a PHI-6-infested cell is set equal to 1, then that of a PHI-H2 phage is almost double (R = 1 and T = 1.99). The fitness of a PHI-H2-defector in a PHI-H2-infested cell turns out to be P = 0.83, and that of a PHI-6-phage in such a cell is S = 0.65. This is precisely the rank ordering required for the prisoner's dilemma.

This was by no means a foregone conclusion, even when one strategy is known to be more cooperative than the other. Suppose, for instance, that two cars are caught in a snowdrift. To cooperate means getting out and starting shovelling. If the other driver does this, you can improve your own payoff by defecting (and staying in your heated car). So T is larger than R. But if the other player defects, you are well advised to get out and start shovelling. This is better than spending the night in the car. Hence S is larger than P, in contrast to the prisoner's dilemma.

In this case we end up with the payoff ranking of the so-called chicken game. In an evolutionary setting, defectors will not take over when playing this chicken game. They can invade a population of cooperators, but cooperators can also invade a population of defectors. The outcome is a mixed population. Examples of viral 'chicken' defectors have been known for a while. They quite literally have a defect that means that they cannot reproduce in the absence of complete viruses; in a population consisting entirely of their own kind, their fitness is zero. In this case, S is larger than P = 0, and we have a chicken game instead of a prisoner's dilemma.

It seems to us that such a possibility should also be tested carefully in interactions among animals with a cognitive apparatus: in such cases it is likely that a social norm will evolve which determines which of the two players does the cooperating and which does not. For instance, if two lionesses are jointly engaged in territorial defence of their pride, one may consistently be bolder than the other in carrying out defensive duties. If the cost of losing the territory is higher than the risk of an injury, this would be precisely what the theory predicts.

Game theory purists may still quibble that Turner and Chao's matrix does not satisfy the condition 2R > T + S. This condition is usually added to the definition of the prisoner's dilemma to rule out the possibility that one of the two players cooperates, the other defects, and both then share their total payoff. With phages, this is not to be feared because it exceeds their capabilities. Another technical objection is that the phages crowded in the bacterial cell are not engaged in a pairwise contest, the usual context of the prisoner's dilemma. Again, this is no serious matter. What counts is that, whatever the ratio of defecting to cooperating phages in a cell, defectors always have an advantage. Necessarily, they will multiply faster, to the detriment of the average fitness.

So why haven't they taken over? Why is the predominant form the good, helpful PHI-6 rather than its lazy cousin PHI-H2? We know little about the ecology of PHI-6 (even its natural bacterial host is unknown). But the origin of the defector gives us a clue, for the mutant PHI-H2 evolves only if the multiplicity of infection is high; that is, if there are many phages invading each host cell. In such circumstances, a phage is likely to find itself in a host cell together with phages from another clone, and then it pays to exploit them. In contrast, if the multiplicity of infection is low, the potential suckers are probably closest kin, members of the same clone, and exploitation would be ultimately self-defeating.

It should be noted, however, that the life cycle of phage PHI-6 (reproducing in bacteria which eventually burst, and reentering new bacteria) marks it as an ideal candidate for a specific type of group selection — which can, more orthodoxly, be viewed as individual-based selection for the ability to build successful groups. Is cooperation due to being related or to being in the same boat? Even non-related phages may be better off by cooperating, and producing their full share of intracellular products, if the defective PHI-H2 has an edge in the competition within the cellular compartment only, and not over the full life cycle. Exploring this issue calls for further experiments with artificially increased competition based on high multiplicity of infection: these phages may become a testing ground for arguments on kin selection versus group selection, or on the evolution of virulence, just as they have been used for studying sexual recombination.

Finally, we recall that the role of compartments in sheltering cooperators from being exploited is crucial to certain hypotheses on the origin of life. Today, phages are arguably the simplest players of the prisoner's dilemma. But it is conceivable that, a few billion years ago, still more primitive molecules were engaged in that game.

Nature Macmillan Publishers Ltd 1999